Yes, that is what it does.
Of course, this creates a problem for anyone without an offical ID. Like someone here illegally. They can't generate these tokens.
Ah, but actually there's a further wrinkle to it:
Suppose I send such a proof to the tobacco store. If the tobacco store later shares that proof with the EU, will the EU be able to determine that the person who sent the proof to the tobacco store was me?
Suppose I send such a proof to the tobacco store. If the tobacco store later shares that proof with the EU, will the EU be able to determine that the person who sent the proof to the tobacco store was me?